Glassy Mean-Field Dynamics of the Backgammon model

TL;DR

This paper provides an exact analytical study of the relaxation dynamics in the backgammon model, revealing glassy behavior caused by entropy barriers and extending the analysis to variants with energy barriers.

Contribution

It offers a complete analytical treatment of the model's dynamics in infinite dimensions, including derivations of evolution equations and autocorrelation functions.

Findings

Demonstrates glassy phenomena due to entropy barriers

Derives a closed-form evolution equation for occupation probabilities

Analyzes effects of energy barriers in model variants

Abstract

In this paper we present an exact study of the relaxation dynamics of the backgammon model. This is a model of a gas of particles in a discrete space which presents glassy phenomena as a result of {\it entropy barriers} in configuration space. The model is simple enough to allow for a complete analytical treatment of the dynamics in infinite dimensions. We first derive a closed equation describing the evolution of the occupation number probabilities, then we generalize the analysis to the study the autocorrelation function. We also consider possible variants of the model which allow to study the effect of energy barriers.